We present a measurement of the isolated direct photon cross section in pp¯ collisions at s√=1.8  TeV and |η|<0.9 using data collected between 1994 and 1995 by the Collider Detector at Fermilab (CDF). The measurement is based on events where the photon converts into an electron-positron pair in the material of the inner detector, resulting in a two track event signature. To remove π0→γγ and η→γγ events from the data we use a new background subtraction technique which takes advantage of the tracking information available in a photon conversion event. We find that the shape of the cross section as a function of photon pT is poorly described by next-to-leading-order QCD predictions, but agrees with previous CDF measurements.